I don't think empathy needs to be emotionally draining. I observe that some people are highly empathetic yet not dragged down by it at all: once they finish assisting or meeting a suffering person, they have undaunted joy and energy. Since realizing this I've tried to emulate them, at least on the not-dragged-down side of the equation. I think I've made progress. I don't know how - my self-insight isn't great - but maybe just by seeing it as possible.
For what it's worth, your definitions of the terms match the ones I've seen.
Today's post, Sympathetic Minds was originally published on 19 January 2009. A summary (taken from the LW wiki):
Discuss the post here (rather than in the comments to the original post).
This post is part of the Rerunning the Sequences series, where we'll be going through Eliezer Yudkowsky's old posts in order so that people who are interested can (re-)read and discuss them. The previous post was In Praise of Boredom, and you can use the sequence_reruns tag or rss feed to follow the rest of the series.
Sequence reruns are a community-driven effort. You can participate by re-reading the sequence post, discussing it here, posting the next day's sequence reruns post, or summarizing forthcoming articles on the wiki. Go here for more details, or to have meta discussions about the Rerunning the Sequences series.